Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula
This work is devoted to the bending analysis of functionally graded (FG) nano-scale plate by using the nonlocal mixed variational formula under simply supported edge conditions. According to Eringen’s nonlocal elasticity theory, the mixed formula is utilized in order to obtain the governing equation...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/7/1162 |
| _version_ | 1797562410148560896 |
|---|---|
| author | Ashraf M. Zenkour Zahra S. Hafed Ahmed F. Radwan |
| author_facet | Ashraf M. Zenkour Zahra S. Hafed Ahmed F. Radwan |
| author_sort | Ashraf M. Zenkour |
| collection | DOAJ |
| description | This work is devoted to the bending analysis of functionally graded (FG) nano-scale plate by using the nonlocal mixed variational formula under simply supported edge conditions. According to Eringen’s nonlocal elasticity theory, the mixed formula is utilized in order to obtain the governing equations. The system of equations is derived by using the principle of virtual work. The governing equations include both the small and the mechanical effects. The impact of the small-scale parameter, aspect and thickness nano-scale plate ratios, and gradient index on the displacement and stresses are explored, numerically presented, and discussed in detail. Different comparisons are made to check the precision and validity of the bending outcomes obtained from the present analysis of FG nano-scale plates. Parametric examinations are then performed to inspect the impacts of the thickness of the plate on the by and large mechanical reaction of the practically evaluated plates. The displayed outcomes are valuable for the configuration procedures of keen structures and examination from materials. |
| first_indexed | 2024-03-10T18:27:48Z |
| format | Article |
| id | doaj.art-97176a156b184091895da8e0798a7ba6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:27:48Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-97176a156b184091895da8e0798a7ba62023-11-20T06:51:15ZengMDPI AGMathematics2227-73902020-07-0187116210.3390/math8071162Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational FormulaAshraf M. Zenkour0Zahra S. Hafed1Ahmed F. Radwan2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Khaled University, Abha 21589, Saudi ArabiaDepartment of Mathematics and Statistics, Higher Institute of Management and Information Technology, Nile for Science and Technology, Kafrelsheikh 33514, EgyptThis work is devoted to the bending analysis of functionally graded (FG) nano-scale plate by using the nonlocal mixed variational formula under simply supported edge conditions. According to Eringen’s nonlocal elasticity theory, the mixed formula is utilized in order to obtain the governing equations. The system of equations is derived by using the principle of virtual work. The governing equations include both the small and the mechanical effects. The impact of the small-scale parameter, aspect and thickness nano-scale plate ratios, and gradient index on the displacement and stresses are explored, numerically presented, and discussed in detail. Different comparisons are made to check the precision and validity of the bending outcomes obtained from the present analysis of FG nano-scale plates. Parametric examinations are then performed to inspect the impacts of the thickness of the plate on the by and large mechanical reaction of the practically evaluated plates. The displayed outcomes are valuable for the configuration procedures of keen structures and examination from materials.https://www.mdpi.com/2227-7390/8/7/1162FG nano-scale platenonlocal theorymixed variational formulabendingNavier’s methodanalytical solutions |
| spellingShingle | Ashraf M. Zenkour Zahra S. Hafed Ahmed F. Radwan Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula Mathematics FG nano-scale plate nonlocal theory mixed variational formula bending Navier’s method analytical solutions |
| title | Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula |
| title_full | Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula |
| title_fullStr | Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula |
| title_full_unstemmed | Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula |
| title_short | Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula |
| title_sort | bending analysis of functionally graded nanoscale plates by using nonlocal mixed variational formula |
| topic | FG nano-scale plate nonlocal theory mixed variational formula bending Navier’s method analytical solutions |
| url | https://www.mdpi.com/2227-7390/8/7/1162 |
| work_keys_str_mv | AT ashrafmzenkour bendinganalysisoffunctionallygradednanoscaleplatesbyusingnonlocalmixedvariationalformula AT zahrashafed bendinganalysisoffunctionallygradednanoscaleplatesbyusingnonlocalmixedvariationalformula AT ahmedfradwan bendinganalysisoffunctionallygradednanoscaleplatesbyusingnonlocalmixedvariationalformula |